Smallest Known Oscillators to p106 (and Beyond)

[Period1GliderGun]

59p272 (previous record was 60):

Code: Select all

x = 23, y = 32, rule = B3/S23
12b2o$12b2o2$10b4o$10bo2bo4$bo$b3o12bo$4bo12bo$3b2o9bo2bo$14b3o4$2b2o
$bobo$bo$2o$19b2o$19bo$20b3o$7b3o12bo2$2b2ob2o$2b2obobo$8bo$3bo4bo$3b
o4bo$4bo2b2o$7b2o!

86p308:

Code: Select all

x = 39, y = 23, rule = B3/S23
2b2o5bo$o2bo4bo$9bo2b2o8b2o$6b2obobo2bo6bo9b2o$o4b2o2b2o4bo8bo6bo$bo2b
obob2o12b2o5bobo$2b2o2bo22b2o$7bo4bo2bo$6bo5b2o2$23bo8bo$14b2o4b2o10b
2o$14b2o3bo3b2o3b2o3bo3b2o$19b2o10b2o4b2o$20bo8bo4$22b2o$21bobo5b2o$21b
o6bo$20b2o9bo$29b2o!

[Period1GliderGun]

I spent a week combing through the SKOP table looking for LCMs to reduce. Here are 13 results in the 300-500 range.

63p336:

Code: Select all

x = 35, y = 32, rule = B3/S23
20b2o$17bo2b2o$16bo4bo$16bo4bo$21bo$15b2obobo$15b2ob2o2$20b3o4$31bo$29b
3o$28bo$2o26b2o$bo$bobo15b3o$2b2o$18bo2bo$19b2o3$14b2o$13bo2bo$31b2o$
13b3o15bobo$33bo$5b2o26b2o$6bo$3b3o$3bo!

107p339:

Code: Select all

x = 56, y = 37, rule = B3/S23
52b2o$52bo$50bobo$50b2o7$37b2o14b2o$19b2o4b2o10b2o8bobo3b2o$19b2o4b2o
21b2o$7b2o39bo$7b2o$37b2o$7b4o24bo2bo13b2o$2b2o2bo3bo24bo16bo$2b2o2b2o
17b3o7b3o15b3o$27bo27bo$24bo2bo$24b2o2$2b3o9bo$o12b2o21b2o4b2o$o4bo2b
2o3bobo8b2o10b2o4b2o$bo6b2o14b2o$3b2o$4bo$4bo$4bo3$11b2o$10bobo$10bo$
9b2o!

106p357:

Code: Select all

x = 57, y = 45, rule = B3/S23
24b2o$24b2o$19bo$17b3o$16bo25b2o$16b2o24b2o3$2b2o$2b2o$25bo$24b3o$23b
o3bo$23b2ob2o19b2o$47bobo$2o47bo$bo47b2o$bobo$2b2o19b2ob2o$23bo3bo$24b
3o$25bo$47b2o$47b2o3$7b2o24b2o$7b2o25bo11b2o$31b3o12b2o$31bo$25b2o15b
o$25b2o14bobo$42bo4bob2o$47bo3bo$47bo3bo$48b3o$47b3o$46bo3bo$46bo3bo$
47b2obo4bo$54bobo$55bo2$50b2o$50b2o!

100p364:

Code: Select all

x = 38, y = 23, rule = B3/S23
22b3o$31bo$19bo2bo6b3o$19bo3bo4bo$28b2o2$6bo5b2o$7bo4bo2bo17b3o$2b2o2b
o25b3o$bo2bobob2o$o4b2o2b2o4bo6b3o$6b2obobo2bo7bobo$9bo2b2o8bo2bo$o2b
o4bo14bobo$2b2o5bo7b2o4b3o$17bo16b2o$14b2obo17bo$14bob2ob2o14bobo$19b
o8b2o6b2o$19bobo6b2o2b2o$20b2o10bobo$34bo$34b2o!

96p399:

Code: Select all

x = 59, y = 45, rule = B3/S23
52bo$52bo$52bo$51b2o$49bo$45bo2bo4bo$32b2o9b3o2bo$33bo8bo7b3o$33bobo6b
2o$34b2o$29b2o$29b2o2$51b3o2$55b2o$37b3o15bobo$38bo18bo$36b2o19b2o$36b
o$21b2o$20bobo$20bo$19b2o3$38b2o$38bo$36bobo$36b2o$22bo$2o19b2o$bo18b
o$bobo15b3o$2b2o2$5b3o2$28b2o$28b2o$23b2o$15b2o6bobo$16bo8bo$13b3o9b2o
$13bo!

88p406:

Code: Select all

x = 47, y = 30, rule = B3/S23
31bo$29b3o$28bo$28b2o6b2o$36bo$34bobo8b2o$34b2o9b2o3$26b2o$25bobo$6bo
5b2o11bo$7bo4bo2bo9bobo$2b2o2bo19b2o$bo2bobob2o$o4b2o2b2o4bo$6b2obobo
2bo28b2o$9bo2b2o29bobo$o2bo4bo36bo$2b2o5bo33bobo$43b2o3$24b2o9b2o$24b
2o8bobo$34bo$33b2o6b2o$42bo$39b3o$39bo!

76p418:

Code: Select all

x = 38, y = 25, rule = B3/S23
24bo$23bo2bo$23bo2bo2bo$25bo3bo$29bo3$11bo$11b3o$14bo14bo$7bo5b2o14b2o
$6bobo19b2o$7bo$19b2o$5b5o8b2o14b2o$4bo5bo8bo14bo$3bob2obo2bo23b3o$3b
obobo29bo$2obobobo$2obobobo$4bo6bo7bo$9b2obo6bo3bo$12bo6bo2bo2bo$12b2o
8bo2bo$24bo!

98p425:

Code: Select all

x = 68, y = 29, rule = B3/S23
44b2o4b2o$44bobo2bobo$46bo2bo$45bo4bo$18b2o25bo4bo$18bo26bo4bo$15b2ob
o5b2o21b2o$17bo6b2o41bo$10bo54b3o$10b2o3bo48bo$13bo24bo25b2o$11b3o23b
2o$38b2o4$6b3o41b2o$6bo44b2o$4bo3b2o14b2o25bo$9bo15bo$2bo19b3o$bob2o17b
o41b2o$bo39b2o21b2o$2o37bo4bo$39bo4bo$39bo4bo$40bo2bo$38bobo2bobo$38b
2o4b2o!

60p440:

Code: Select all

x = 30, y = 20, rule = B3/S23
2o$2o3$11bo$10bo2bo$13bo8bo$9b2obo8bobo$3b2o4b2o11bo$bob2o$o19b5o$o2b
o15bo5bo$2bo15bo2bob2obo$22bobobo$22bobobob2o$12b2o8bobobob2o$12b2o4b
o6bo$17bob2o$17bo$16b2o!

68p462:

Code: Select all

x = 24, y = 40, rule = B3/S23
9bo$7b3o$6bo$6b2o2$4bo$3bobo$2bo3bo$2bo2bo$2bo2bo$3b2o6$5b2o$4bo2bo$4b
o2bo$3bo3bo$4bobo$5bo$13b2o$2b2o9b2o$3bo$3o6bo$o7bobo$9bo2$13b3ob2o$12b
o3bo2bo$12bo2bo3bo$13b2ob3o2$22bo$21bobo$22bo2$17b2o$17b2o!

104p473:

Code: Select all

x = 58, y = 27, rule = B3/S23
33bo$33b3o$17bo18bo$17b3o15b2o$20bo$19b2o25b2o$2bo43b2o8b2o$bobo9b2o41b
o$bobo4bo5bo39bobo$2ob2obo4b3o40b2o$2bo2bo5bo39bo$2bobo20bobo23bo$3bo
2bo18bobo23bo$4b3o2bo15b3o9b3o$7bo5bo23bobo$4b2o7bo23bobo$4bo8bo$5bo3b
2o$4b2o2bobo$8bo$7b2o8b2o$17b2o25b2o$44bo$28b2o15b3o$28bo18bo$29b3o$31b
o!

108p494:

Code: Select all

x = 36, y = 32, rule = B3/S23
13bo$11bo2bo$8bo2bo2bo$8bo3bo$8bo3$26bo$24b3o$8bo14bo$7b2o14b2o$8b2o$
32bo$17b2o11b3o$2b2o14b2o9bo$3bo14bo10b2o$3o$o26bo$27bo$27bo$18bo$14b
o3bo$12bo2bo2bo$12bo2bo5bo5bo5bo$13bo6bobo2b2ob2o2bobo$20bobo2b2ob2o2b
obo$19b2obobobobobobob2o$20bo2b2obobob2o2bo$20bo4b2ob2o4bo$21b3o7b3o$
23bob2ob2obo$24bobobobo!

62p495:

Code: Select all

x = 32, y = 24, rule = B3/S23
28bo$28b3o$26b2o3bo$25bo2b3o$19bob2obobobo$19b2obobo2bo$24b2o2bo$9b2o
12bo$9b2o18bo$24bo2$27b2o$9b3o16bo$8bo3bo14bo$8b2ob2o14b2o2$bo$obo$2o
3$7b8o$7bob4obo$7b8o!

[rattlesnake]

SKOP 115 Improved: 92P115

Code: Select all

x = 25, y = 28, rule = B3/S23
4bo$4b3o5bo$7bo4bo$6b2o4bo2$18b2o$2b2o14bo$2bo13bobo$4bo11b2o$3b2o6bo
$2bo6b3o$bob2o4bobo$o2bobo5bo$2o2bo2$15b2ob2o$8b2o5b2obobo$9bo8bobo$6b
3o6b2o3b2ob2o$6bo7bo2b2o5bo$14b2o3b2o$16b2obo$16bo2b4o$17bobo3bo$16b2o
bob2o$18bobo$18bobo$19bo!

xp115_y032acy0ezw6ioy2gy0c871zca16a4x317zy2o8a6y0gbbgn1e808ozya11mq0v5kk8zye343

[Period1GliderGun]

137p95:

Code: Select all

x = 32, y = 29, rule = B3/S23
16b2o$16bobo$13b2obo2bo5bo$13bobobobo4bobo$15bo4bo3bobo$15bob4o2b2ob2o
$16bo3bo2bo$17b3ob2ob4o$19bo4bo3bo$27bobo$16bo3bo2bo3bobo$14b3o9b2o2b
2o$13bo11bo2bobo$13b2o9bob3obo$24bo4bo$10bo15b3o$b2o7b2o8bo5bo2b3o$bo
bo16bo6b2o2bo$3bo7bo8bo7bo$3b2o6bo16bobo$b2o2bo5bo8b2o7b2o$o2b3o15bo$
obo4bo$bob3obo9b2o$3bo2bo11bo$bo2b2o9b3o$b2obo10bo$4bo$4b2o!

[WhiteHawk]

137p95:

Code: Select all

Cribbage needs to be updated

[Period1GliderGun]

137p95:

Code: Select all

Cribbage needs to be updated

Done: https://conwaylife.com/wiki/Cribbage#LCM_oscillators

[Period1GliderGun]

115p398:

Code: Select all

x = 59, y = 45, rule = B3/S23
23b2o16b2o$23b2o7b2o7b2o$32b2o5$7b2o48b2o$7b2o48b2o2$3bo$2bobo20bo14b
o$2bobo20b3o10b3o$2o2b2o$bobo2b2o18b3o8b3o$o2b2obobob2o$b2o3bob2obo$3b
2obo$3bob2o$15b2o32b2o$15b2o32b2o4$15b2o32b2o$15b2o32b2o5$26b3o8b3o2$
25b3o10b3o$25bo14bo3$7b2o48b2o$7b2o48b2o5$32b2o$23b2o7b2o7b2o$23b2o16b
2o!

[confocaloid]

Pentadecathlon ID-style descriptors are traditionally uppercased (e.g. "115P398"), in particular on the wiki.
Abbreviations like "p<N>" for "period-<N>" are traditionally lowercased (e.g. "a p398 oscillator").

[Period1GliderGun]

Thanks Confocaloid. I'll do that in the future, starting off with 83P166:

Code: Select all

x = 40, y = 27, rule = B3/S23
24b2o$4b2o5b2o11bo$3bobo6bo9bobo$3b2o7bobo7b2o$b2o10b2o$obo27b2o$2o4b
2o23bo$5bobo20b3o$5b2o21bo2$18b2o$17bobo$17bo2bo4bo$18b2o5b2o$19bo4bo
2bo$6b2o17bobo10b2o$7bo17b2o11b2o$4b3o$4bo11bo$14b3o$13bo$13b2o$30b2o
$21b2o7bobo$20bobo9bo$20bo11b2o$19b2o!

EDIT:
79P528, just to clear up the ambiguity of having multiple 81-cell SKOPs:

Code: Select all

x = 37, y = 25, rule = B3/S23
22b2o$22bo5b2o$12b2o5b2obo5b2o$2bo10bo5bobo$bobo9bob2o$bobo10bobo$2ob
obo5b3o$2bo3bo4bo$2bob3o$3bo3bo$4b4o13b3o$22b2o$4b2o17b4o$4bo21b2o$5b
o20b3o$4b2o4$33bob2o$33b2obo$28bobo$20b2o5bob2o$20b2o5bo$26b2o!

EDIT2:
128P411:

Code: Select all

x = 76, y = 58, rule = B3/S23
67bo$66bobo$67bo2$65b5o$43b2o20bo4bo$44bo23bo2bo$44bobo21b2obo2bo$45b
2o18bo5bobobo$64bobo4bo2bo$64bo2bo2b2o$65b2o$34b2o$35bo$35bobo$36b2o$
49b3o$49bo$49b3o2$30bo$29bobo$29bobo$30bo7$45bo$44bobo$44bobo$45bo2$24b
3o$26bo$24b3o$38b2o$38bobo$40bo$40b2o$9b2o$4b2o2bo2bo$bo2bo4bobo$obob
o5bo18b2o$bo2bob2o21bobo$4bo2bo23bo$5bo4bo20b2o$6b5o$19b3o$8bo8bo$7bo
bo7bo4bo$8bo9bo$20b2o$21bo$21bo$21bo!

128P447:

Code: Select all

x = 79, y = 61, rule = B3/S23
70bo$69bobo$70bo2$68b5o$46b2o20bo4bo$47bo23bo2bo$47bobo21b2obo2bo$48b
2o18bo5bobobo$67bobo4bo2bo$67bo2bo2b2o$68b2o$37b2o$38bo$38bobo$39b2o$
52b3o$52bo$52b3o5$30bo$29bobo$29bobo$30bo4$48bo$47bobo$47bobo$48bo5$24b
3o$26bo$24b3o$38b2o$38bobo$40bo$40b2o$9b2o$4b2o2bo2bo$bo2bo4bobo$obob
o5bo18b2o$bo2bob2o21bobo$4bo2bo23bo$5bo4bo20b2o$6b5o$19b3o$8bo8bo$7bo
bo7bo4bo$8bo9bo$20b2o$21bo$21bo$21bo!

This gives oscillators with at most 128 cells for all periods of the form 3*(4n+1).

89P297:

Code: Select all

x = 30, y = 37, rule = B3/S23
27bo$26bobo$22bo3bobo$15bob2obobo2b2ob2o$15b2obobo3bo2bo$19b3o3bobo$20b
2o4bo$15b2o3b6o$15bo2bo3bo$24b2o$25bo$13bo4bo5bo$13bo2b2o6b2o$13b2o$9b
2o$9b3o6bobo$8bo3bo8b2o$11b3o2b2o3b2o$bo2bo3bo3bo4bobobo$5bo4b2o6b3o$
o4bo4bo8bo3b3o$2o21bo$6bo21b2o$4b3o3bo8bo4bo4bo$9b3o6b2o4bo$8bobobo4b
o3bo3bo2bo$7b2o3b2o2b3o$7b2o8bo3bo$9bobo6b3o$19b2o$15b2o$12b2o2bo$11b
o4bo3$11bo2bo$13b2o!

72P198:

Code: Select all

x = 18, y = 34, rule = B3/S23
10b2o$7b2o2bo$7bo3bobo$8b3obobo$10bo3bo$6b3obo3bob2o$5bo2bobo3bob2o$o
4b2o2b2obobo$3o10b2o$3bo$2b2o2$5bo$4bobo$3bo3bo$4bo2bo$4bo2bo$5b2o6$3b
2o$2bo2bo$2bo2bo$2bo3bo$3bobo$4bo2$6b2o$6bo$7b3o$9bo!

67P220:

Code: Select all

x = 21, y = 34, rule = B3/S23
10b2o$10b2o3$10bo$10b2o$bo8bobo$b3o7b2o$4bo5bobo5b3o$3b2o6b2o4b3o6$b3o
4b2o6b2o$3o5bobo5bo$8b2o7b3o$8bobo8bo$9b2o$10bo2$2b2o$2bo6b2o$4bo4b2o
$4bobo2$6bobo2$8bobo2$10b2o$13bo$12b2o!

EDIT3:
110P237 and 114P395 based on unexpecred:

Code: Select all

x = 82, y = 62, rule = B3/S23
24b2o$24bobo2b2o38b2o$26bo3bo38bobo2b2o$22b4ob3o41bo3bo$21bo3bobo39b4o
b3o$21b2o2bobob3o34bo3bobo$26b2obo2bo33b2o2bobob3o$31b2o38b2obo2bo$76b
2o3$15b2o$15b2o43b2o$8b2o50b2o$9bo43b2o$9bobo42bo$5b2o3b2o42bobo$4bo50b
2o$7bo$3bo3bo$4o3bo$5bo14bobo$22bo42bobo$67bo$20b3o$21bo43b3o$66bo7$53b
o2bo$52bob2obo$23bo29bo2bo$22b3o28bo2bo11bo$52bob2obo9b3o$22bo30bo2bo
$22bobo42bo$67bobo4$33b2o$33bobo42b2o$35bo42bobo$35b2o43bo$28b2o50b2o
$28b2o43b2o$73b2o3$12b2o$12bo2bob2o38b2o$13b3obobo2b2o33bo2bob2o$17bo
bo3bo34b3obobo2b2o$15b3ob4o39bobo3bo$14bo3bo41b3ob4o$14b2o2bobo38bo3b
o$19b2o38b2o2bobo$64b2o!

EDIT4:
86P182, by Entity Valkyrie 2:

Code: Select all

x = 39, y = 19, rule = B3/S23
16b2o3b2o$15b2obobob2o$18bobo$18bobo2$17b2ob2o2$16bo5bo$14bo2bo3bo2bo
$5b2o11bobo11b2o$5bobo6bo9bo6bobo$6b2o7bo7bo7b2o$2b2o12bobobobo12b2o$
bobo5b2o4b2o5b2o4b2o5bobo$bo6bobo5b2o3b2o5bobo6bo$2o6bo21bo6b2o$6b3o21b
3o$5bo10b2o3b2o10bo$5b2o9b2o3b2o9b2o!

EDIT5: 94P158:

Code: Select all

x = 38, y = 53, rule = B3/S23
26b2o$26bo$24bobo$24b2o$28b2o$28b2o2$35bo$35bobo$34bobo$6b2o12bo15bo$
6b2o12b2o$22bo$20b2o$20bo$36b2o$32b2obobo$32b2obo$36bo$32b2ob2o$33bob
o$33bobo$34bo8$3bo$2bobo$2bobo$b2ob2o$bo$2bob2o$obob2o$2o$17bo$16b2o$
15bo$16b2o12b2o$bo15bo12b2o$bobo$obo$2bo2$8b2o$8b2o$12b2o$11bobo$11bo
$10b2o!

[Period1GliderGun]

146P178, just barely squeaking by the 148-cell rectifier loop:

Code: Select all

x = 42, y = 42, rule = B3/S23
19b2o$7bo5bob2obo2bo$7b3o3b2obob2obo$10bo10bobo$3b2o4b2o6b2obob2o$4bo
12b2obo$4bobo13bo$5b2o13b2o2$8b2o$7bo2bo$8bobo$9bo$21b2o$21bobo$7b2o14b
o$2obobo2bo14b2o$ob2ob3o17bo$4bo16bo3b3o9b2o$4bob2o14bo5bo8bo$5bobo12b
3o4b2o5bo3b3o$34b4o3bo$39bobo$36b2ob2o$36b2o$39b2o$40bo$39bo$39b2o3$30b
2o5b2o$29bo2bo4bobo$25b2o3bobo6bo$21b2obobo4bo7b2o$22bobo9b2o$21bo2b2o
8bo$22b2o11b3o$24b2o11bo$24bo$25bo$24b2o!

EDIT: 77P576, replacing a 48P9 with a 22P36:

Code: Select all

x = 42, y = 39, rule = B3/S23
25b2o$26bo6bo$26bobo4bo$27b3o3bo$29bo$29b3o3b3o2$33bo$30b4o$30b4o$30b
o2$26b3o3b3o$34bo$30bo3b3o$30bo4bobo$30bo6bo$37b2o3$17b2o$17b2o3$16bo
21b2o$6b2o8bo$16bo20bo3bo$5bo3bo26bo4bo$4bo4bo25bobobo$3bobobo26bobob
o$2bobobo14b2o9bo4bo$o4bo16b2o8bo3bo$o3bo11bo4b2o$14b3o17b2o$2b2o6b2o
2bo$10b2o2bo$15bo3bo$19bo3b2o$23b2o!

[galoomba]

146P178, just barely squeaking by the 148-cell rectifier loop:

Code: Select all

x = 42, y = 42, rule = B3/S23
19b2o$7bo5bob2obo2bo$7b3o3b2obob2obo$10bo10bobo$3b2o4b2o6b2obob2o$4bo
12b2obo$4bobo13bo$5b2o13b2o2$8b2o$7bo2bo$8bobo$9bo$21b2o$21bobo$7b2o14b
o$2obobo2bo14b2o$ob2ob3o17bo$4bo16bo3b3o9b2o$4bob2o14bo5bo8bo$5bobo12b
3o4b2o5bo3b3o$34b4o3bo$39bobo$36b2ob2o$36b2o$39b2o$40bo$39bo$39b2o3$30b
2o5b2o$29bo2bo4bobo$25b2o3bobo6bo$21b2obobo4bo7b2o$22bobo9b2o$21bo2b2o
8bo$22b2o11b3o$24b2o11bo$24bo$25bo$24b2o!

144P178 with a smaller jubjub variant:

Code: Select all

x = 43, y = 43, rule = B3/S23
20b2o$19bo2bo$7bo8b2o2bobo$7b3o6bob2obo$10bo10bobo$3b2o4b2o6b2obob2o$
4bo12b2obo$4bobo13bo$5b2o13b2o2$12bo$11b3o$11bobo2$21b2o$21bobo$5b3o
15bo$2obobo2bo14b2o$ob2ob3o17bo$4bo20b3o9b2o$4bob2o20bo8bo2b2o$5bobo
19b2o5bo3b2o2bo$34b4o2bobo$39bobo$36b2obo$36b2o2bo$39b2o6$30b2o5b2o$
29bo2bo4bobo$25b2o3bobo6bo$21b2obobo4bo7b2o$22bobo9b2o$21bo2b2o8bo$22b
2o11b3o$24b2o11bo$24bo$25bo$24b2o!

[WhiteHawk]

edit: Pentadecathlon on 42p38

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This p570 oscillator was previously recognized over a year ago by C28, though the current p570 in the SKOP collection on the Wiki still lists Pentadecathlon on Raucci's P38 as the smallest p570 oscillator. It any case, it was never posted here, and the sparking component is slightly unusual.

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x = 39, y = 23, rule = B3/S23
24b3o$25b3o$29b3o4$12bo$12b3o$15bo14b2o$14b2o15bo$29b3o$2bo4bo$2ob4ob
2o9b3o$2bo4bo11bo15b2o$19b2o14bo$36b3o$38bo4$19b3o$23b3o$24b3o!

EDIT: Here is a p2280 oscillator which utilizes said sparking capability with only 66 cells - not sure if this is SKOP2280 due to Pentadecathlon shuttles and Boojum reflector, but perhaps there is a different SKOP which could utilize the interaction.

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x = 39, y = 26, rule = B3/S23
25bo$24bo2bo$24bo2bo2bo$26bo3bo$30bo3$12bo$12b3o$15bo14bo$14b2o14b2o$
29b2o$2bo4bo$2ob4ob2o10b2o$2bo4bo11b2o14b2o$20bo14bo$36b3o$38bo3$11b2o
7bo$9bob2o7bo3bo$8bo11bo2bo2bo$11bo11bo2bo$7b2obo14bo$7b2o!

EDIT 2:

The lowest period which currently has a SKOP with a minimum population higher than it's period is now 131, achieved by the following rectifier loop with minpop 136.

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Below p131, 63 periods have SKOPs with minimum populations higher than their period: 1-14, 16-23, 25-29, 31-35, 37-39, 41-44, 47, 50-51, 53, 57, 59, 61-63, 67, 69, 71, 74, 79, 81, 89, 95, 97, 101, 103, 109, and 121. The only period where the SKOP's minimum population currently matches it's period is Caterer on Figure Eight (p24)

Previously updated to the SKOP table in 2024, but never mentioned here: SKOP142 at 125 cells, which gives p131 rectifier loop as the highest-period SKOP with a minimum population greater than it's period.

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x = 49, y = 32, rule = B3/S23
32bo$30b3o$20b2o7bo$19bobo7b2o$19b2o2$8bo24bo$7bobo23bo$8bo24bo$29b2o
$6b5o18b2o4b3o$5bo4bo2bo15bobo$4bo2bo5b3o14bo$bo2bob2o8bo13bo$obobo5b
o4b2o21b2o$bo2bo4bobo25bo2bo2b2o$4b2o2bo2bo25bobo4bo2bo$9b2o21b2o4bo5b
obobo$14b3o15bo8b2obo2bo$33b3o5bo2bo$12bo5bo16bo2bo4bo$12bo5bo19b5o$12b
o5bo$40bo$14b3o22bobo$40bo2$28b2o$18b2o7bobo$19bo7b2o$16b3o$16bo!

Also SKOP134 at 125 cells

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x = 48, y = 31, rule = B3/S23
16bo$16b3o8bo$19bo8bo$18b2o7bobo$28bobo$39bo$38bobo$39bo2$15bo21b5o$13b
2ob2o16bo2bo4bo$15bo16b3o5bo2bo$21bobo7bo8b2obo2bo$22b2o7b2o4bo5bobob
o$9b2o11bo13bobo4bo2bo$4b2o2bo2bo24bo2bo2b2o$bo2bo4bobo20bo4b2o$obobo
5bo4b2o15bo$bo2bob2o8bo15bo$4bo2bo5b3o$5bo4bo2bo14b3o3b3o$6b5o$32bo$8b
o23bo$7bobo22bo$8bo$18b2o$18bobo7b2o$19b2o7bo$29b3o$31bo!

[Period1GliderGun]

87P234, down from (presumably) a 92-cell p6 thumb loop:

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x = 26, y = 30, rule = B3/S23
19b2o$19bobo$20b3o$21b2o$19bobo$14b2o2bobo$14bobo2bo$15b4o$16b2o$2b2o
b2o$3bobo$3bo7b2ob2o$2obo2bo5bobo$bobob3o10b2o$bob2o3bo9b2o$2bo3b2o6b
o$3b3o7bo2bo$5bo4bo6bo$9bo7bo$10bob2o3bo6b2o$14b3o7b2o$19b3o$18bo3bo$
18bo$18bo$19bo2bo$19bo2$19bobo$20bo!

EDIT: 98P224:

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x = 35, y = 22, rule = B3/S23
22bo$20b3o$19bo$19b2o10b2o$29b3o2bo$16b3o9bo4b2o$15bo3bo4bo3b5o$14bo5b
ob3o3b2o2bo$14bo5bo3bo3b4o$5bo8bo5bo7bo3b3o$15bo3bo9b3o2bo$3b3obo8b3o
12bo$2bob2o$2b2obo16b2o$ob3o5b2o10b2o4b2o$10b2o15bob2ob2o$2bo22b3obob
4o2$21b4obob3o$22b2ob2obo$26b2o4b2o$32b2o!

[hotdogPi]

That p224 isn't minimal. Here's the p92-cell p224 from before:

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x = 41, y = 48, rule = B3/S23
4b2o8b2o$4b2o8bo$15bo$4bo9b2o$3b2o8bo$b2o2bo3b2o2b3o$bobo5b2o5bo$bo7b2o4b2o$
8b2o$8b3o$2o4bo$2o3bob2o$7b2o4$4b2o$3bobo$3bo$2b2o9$37b2o$37bo$35bobo$35b2o4$
34b2o$34b2o3b2o$39b2o3$24b2o13bo$24bo5b2o5bobo$25b3o2b2o3bo2b2o$27bo8b2o$25b
2o9bo$25bo$26bo8b2o$25b2o8b2o!

(My database is significantly outdated, from August 24, 2022, and I would like an update, but this is more an issue for confirming "new smallest" claims rather than disproving them.)

[Period1GliderGun]

Thanks HDP. I somehow thought that SKOP 224 was a 116-cell HC0 loop instead of a p8 reflector loop...

118P125; a smaller p25 sparker may exist (30P25 doesn't work):

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x = 36, y = 28, rule = B3/S23
3bob2o4b2obo$3b2o2bo2bo2b2o$b2o3bo4bo3b2o$o3b2ob4ob2o3bo$b3obobo2bobo
b3o$3bobobo2bobobo$6bo4bo$7b4o$18bo4b3o$16b3o$15bo$15b2o13b2o$30b2o$7b
2o2b3o8b3o$7b2o2bobo7bo2bo9bo$12bo7bo3bo4b2o2bobo$11bo8bo8b2o3bo$20bo
3bo$21bo2bo$22b3o2$17b2o$17b2o7b2obo$26b2ob3o$32bo$26b2ob3o$25bo2b2o$
25b2o!

EDIT: 110P377, found specifically to prove one of WhiteHawk's predictions (namely, that at least 2 SKOPs would replace rectifier loops this year):

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x = 33, y = 38, rule = B3/S23
22b2o$22b2o2$25bo2bo$24bo6bo$24bo7bo$16b2o6bo3b2obo$16b2o7b3o$20b3o$13b
2o4bo3bo$13b2o8bo$18bo4bo$19bo2bo$10b2o10bo$11b3o$12b2o6bobo$13bo7bo$
16b2o$7b3o6bobo$2bo15bo$bobo4bobo7b2o$2bo8b2o$10bo$7bo7b2o$7bo7bobo$b
o15bo$o7bo8b2o$o8b2o$bo3b2obo$18b2o$5b3o7b2o2bo$11bo2bob3o$11b4o$8bo6b
4o$8b6obo2bo$12bobo$10bo$10b2o!

[WhiteHawk]

Thanks HDP. I somehow thought that SKOP 224 was a 116-cell HC0 loop instead of a p8 reflector loop...

If it is the case that (EDIT 2: 92)-cell p8 reflector loops beat HC0 loops for population, then SKOPs 352, 416, 472, and 488 are not hotcrystal0-based SKOPs as the HC0 Reaction page suggests (It would be helpful if the mentioned blocker reflector was actually on that page to confirm. I am having trouble manually placing the blocker and doubt it could actually fit in the minimal designs there).

If the previous assertation is correct (EDIT 2: it is), here are the SKOPs for those periods (all with 92 cells)

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x = 292, y = 81, rule = B3/S23
221b2o8b2o$220bo2bo7bo$141b2o8b2o79bo$140bo2bo7bo67bo11b2o$152bo66bo2b
o7bo$139bo11b2o64b2ob2o4b2o2b3o$139bo2bo7bo66b3o6b2o5bo$137b2ob2o4b2o
2b3o65bo13b2o$137b3o6b2o5bo$65b2o8b2o61bo13b2o$65b2o8bo141b2o$76bo140b
2o3b2o$75b2o60b2o83b2o$65bo8bo62b2o3b2o$64b3o3b2o2b3o65b2o$62b2ob2o3b
2o5bo$5b2o8b2o44bo2bo11b2o143b2o$5b2o8bo48bo155bobo$16bo124b2o77bo$15b
2o43bo2bo76bobo76b2o$5bo8bo46b2o3b2o72bo$4b3o3b2o2b3o49b2o71b2o$2b2ob
2o3b2o5bo$bo2bo11b2o$4bo$65b2o$o2bo60bobo$b2o3b2o56bo$6b2o55b2o4$5b2o
$4bobo$4bo$3b2o25$54b2o$41bo12bo67b2o81b2o80b2o$42bo9bobo54bo12bo69bo
12bo68bo12bo$40b3o9b2o56bo9bobo70bo9bobo69bo9bobo$108b3o9b2o69b3o9b2o
68b3o9b2o3$51b2o$51b2o3b2o61b2o81b2o80b2o$55bo2bo60b2o3b2o76b2o3b2o75b
2o3b2o$123bo2bo79bo2bo78bo2bo$54bo$41b2o11bo2bo64bo82bo81bo$41bo5b2o3b
2ob2o52b2o11bo2bo66b2o11bo2bo65b2o11bo2bo$42b3o2b2o3b3o54bo5b2o3b2ob2o
67bo5b2o3b2ob2o66bo5b2o3b2ob2o$44bo8bo56b3o2b2o3b3o70b3o2b2o3b3o69b3o
2b2o3b3o$42b2o68bo8bo73bo8bo72bo8bo$42bo67b2o81b2o80b2o$43bo8b2o56bo82b
o81bo$42b2o8b2o57bo8b2o72bo8b2o71bo8b2o$110b2o8b2o71b2o8b2o70b2o8b2o!

EDIT: Found the post from earlier in the thread which explains how it works. Indeed neither 108 cells or 103 cells beat (EDIT 2: 92) cells and that's that.

A p8 variant of the above found by Kazyan on Discord achieves 108 cells for 128+8n to 240 and 103 for 248+8n. This both ties the fixed SKOP128 and displaces the p256 gun as the smallest SKOP256:

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EDIT 3: A little late, but that's just another copy of 34p7 on 56p27, not 30p25

SKOP175 (34P7 on 30P25) in 64 cells:

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EDIT 4: I think i'll just repost this here.

Given David Raucci's recent discoveries of several small oscillators above the snark limit (p43) and the dishevelled state of the oscillator page on the LifeWiki, I made the following stamp collection of the smallest known non-trivial oscillators:

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Updated version of this charts almost 4 years later at the end of March, 2025. Surprising how many oscillators have been replaced within that time (by my calculations, exactly 55 out of 106, or just over half, have been reduced).

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x = 624, y = 401, rule = B3/S23Super
292.2C90.2C75.2C25.2C25.2C44.2C$292.C91.C76.C26.C26.C45.C$292.C91.C76.
C26.C26.C45.C$292.2C90.2C75.2C25.2C25.2C44.2C2$4.D19.3D17.3D19.D16.5D
16.3D16.5D16.3D17.3D17.D3.3D$3.2D18.D3.D15.D3.D17.2D16.D19.D3.D19.D15.
D3.D15.D3.D15.2D2.D3.D$4.D22.D19.D16.D.D16.D19.D22.D16.D3.D15.D3.D16.
D2.D3.D96.5R2.R57.5F2.3F16.5D2.3D27.5D3.D31.5F.5F16.5D2.3D17.5F.5F15.
5F2.3F10.5D2.3D39.3F3.3F$4.D21.D18.2D16.D2.D17.3D16.4D19.D17.3D17.4D16.
D2.D.D.D100.R.2R61.F.F3.F19.D.D3.D30.D2.2D35.F.F24.D.D3.D20.F5.F19.F.
F3.F13.D.D3.D37.F3.F.F3.F$4.D20.D21.D15.5D19.D15.D3.D17.D17.D3.D19.D16.
D2.D3.D99.R3.R60.F6.F18.D6.D29.D2.D.D34.F2.F23.D2.D23.F5.F19.F2.F3.F12.
D2.D3.D37.F3.F.F3.F$4.D19.D18.D3.D18.D16.D3.D15.D3.D17.D17.D3.D15.D3.
D16.D2.D3.D99.R3.R60.F5.F19.D4.2D30.D.D2.D34.F3.3F20.D2.4D20.F5.F19.F
3.3F13.D3.4D38.3F2.F.F.F$3.3D17.5D16.3D19.D17.3D17.3D18.D18.3D17.3D16.
3D2.3D99.R4.R59.F5.F19.D7.D28.D2.5D32.F7.F18.D3.D3.D18.F5.F19.F3.F3.F
11.D7.D37.F3.F.F3.F$290.R4.R59.F4.F20.D3.D3.D28.D5.D33.F3.F3.F18.D3.D
3.D18.F5.F19.F3.F3.F11.D3.D3.D37.F3.F.F3.F$3.200B87.R3.3R58.F3.5F17.D
4.3D29.D5.D33.F4.3F19.D4.3D19.F5.F19.F4.3F12.D4.3D39.3F3.3F2$3.2A19.A
22.A16.2A17.2A23.2A17.2A16.2B17.2A19.B2A100.336B$3.2A18.BAB20.BAB14.A
2.A16.A.B21.B2A2B15.2A16.3B17.A18.2B.A2B$24.A22.AB14.A.A.AB15.B2A21.4B
31.2B2AB17.A.2A15.BA5B119.2B5.2A47.2A12.A44.A15.A15.2A23.A18.A12.2A23.
A54.A10.2A4.2A$46.2A16.A.BAB15.4B21.A2B15.4A12.2B2ABA15.2A.A.A13.4BA2B
A115.B2.3B5.A41.B6.A13.3A42.3A11.3A16.A23.3A14.3A13.A23.3A30.2A18.3A10.
A.A2.A.A$4.A39.A.2B17.3BA17.ABA15.B3.ABAB11.2A.A.B2.A12.4B.A15.B.2B.A
12.BABA2BAB102.2A10.8B.BA.A40.3B2.BA.A16.A6.B37.A9.A19.A.2A23.A3.2B2A
2B3.A15.A21.A5.A29.A18.A15.A2BA$3.A.A37.A4BA16.ABA19.3B13.2AB.A.BA12.
2A.A3BA.A13.A.4B13.3B3A13.2AB.BA103.A.A9.8B.B2A40.5B.B2A16.2A5.3B35.2A
9.2A19.A2B.4B17.2A3.BA2BAB3.2A14.2A20.6A.A29.A17.2A12.BA4BAB$4.A38.AB
.2B40.ABA12.2ABA2B17.A.A2.A15.AB2A2B10.2A.2B3.2A12.B.B.B.B102.AB2.B6.
10B41.3BA5B17.4B.6B34.5B3.5B21.5BAB16.7B2A7B17.A23.A.A28.2A14.5B12.B2A
2B2AB$45.3A41.3B12.3B2A17.A.3A17.B2A2B10.A2.A.2A.A15.AB.B2A102.5B.14B
40.4B2A3B20.10B35.4B.4B22.BA3B2AB18.12B16.3A2BA16.2A2BA2.2A26.2B14.4B
15.2B2A2B$46.B20.B22.ABA11.4B19.A20.3B14.2A.A2.A14.BA2BABAB101.20B40.
4BA4B19.13B32.5B.5B21.3BA4B.B14.16B13.A2.A3B16.ABA2B2A16.2A8.5B11.7B16.
2B$66.2AB22.BAB34.A20.2B18.2A15.A2BA4B99.21B43.6B20.13B31.6B.6B19.4B3A
6B11.18B11.A.A6B16.3BA.A17.A7.6B8.11B6.2A7.D$66.BABA21.2B.A32.2A57.5B
AB99.21BA44.5B20.13B30.7B.7B19.13B10.18B11.A2.A5BA.2A14.2BA3.2A12.A9.
6B5.15B4.A7.B4.B$64.AB2.2BA22.2A92.2BA.2B99.20B2AB44.5B20.12B5.A14.2A
8.7B.7B8.2A9.13B10.18B9.2A.2ABA3B.2A.A15.B3.B2AB11.2A7.7B2.18B.BA.A5.
BA8B$63.B2A2.BA119.2AB98.2AB.18BABAB43.6B19.12B4.A.A3.2A9.A6.6BA2B.2B
A6B6.A11.13B10.16B11.A.A3.BA22.D3.2B14.AB.7B2A3B.19B.2A5.2BA3B5AB$64.
4B57.2A162.A.AB.23B41.4BA4B18.11B3.2BA2B2.A.A8.A.AB2.6B3AB.B3A6B2.BA.
A11.13B10.16B11.A.A5.D20.6B13.3A8BABA25B7.BA2BA3B2A$65.ABA57.A2B161.A
5.B.B2.3B3A6B2.4B40.3B2A4B18.2B3A6B4.4B4.A9.2AB.7BAB2A.2ABA7B.B2A12.2D
5B3A4B9.16B12.A5.B2AB15.A5BABAB11.A2.B.7BA25B9.3BA6B$66.A60.B.BA157.2A
10.2BA3BA3B5.4B38.5BA3B2.2B15.2BABA10B.6B2A.2A.A6.13B.13B13.3D.B.4BA3B
10.5B6.5B18.4A2B12.BA3BA3BAB4.B6.2A4.6BABA13B2A8B10.2B2A4B$123.6ABAB166.
3BA5BA3B5.4B36.2AB.5B3.BAB14.2BA2BA18B.A.2A6.13B.13B12.2BD4.B2A3BAB10.
16B17.ABAB2AB13.AB2A4BA.2B.B2A10.8B2A13BABA6B4.2A5.7BA$123.A5.3B166.3B
A5BA4B5.4B34.A.AB2.3B.D2BABA14.3BABA15B4.A9.13B.13B12.2BD4.BA5B11.16B
17.2A3B2A13.3BA3B2.3A2B2A10.25BA7B.B2.A6.B2AB2A$124.2A.2AB.B2A164.3BA
5BA5B5.4B6.A26.A6.B3.BA3BA10.2A2.2B3A5B.5B3A2B2.2A10.11B3.11B12.2BCDB
4.4B.2BA9.6BA2BA6B18.B.2BAB14.4B2A2.4B.B9.25BABA8B3A8.2A2B$125.A.A3.B
A.A161.2AB.2BA3BAB2.4B5.4B5.3A23.2A11.BA2B.A9.A4.15BABA3B50.2BA2B9.2A
.A7.18B19.4BA19.A3BAB10.2A.19B.3B2A7B.BA11.2B$125.A.A6.A160.A.AB.3B3A
5.4B5.4B7.A37.A.2BAB4.2A.A.18BA2BA2B13.11B3.11B11.2BABA2B11.A7.5BABA2B
ABA5B18.2B3A2B18.A5B9.A.AB.18B2.7B7.2A$126.A7.2A159.A7.5B4.4B5.4B5.2A
10.2A26.A3BAB3.A.2A.2A6B.10BABA2B12.13B.13B10.3BA3B11.2A6.5B2A4B2A5B16.
3B2AB.2A18.3BA2B9.A4.15B5.6B9.A$294.2A10.2A5.4B5.4B4.5B7.A28.ABA2B8.A
4.4B4.6B3A2B12.13B.13B9.4BA4B19.4BA6BA4B17.2A.B2A3B18.B2A3B8.2A6.11B8.
6B7.A$306.A7.4B5.4B5.3A3B.BA.A28.BAB10.A.A2.2BA2B3.11B12.13B.13B9.4BA
4B21.12B19.2B3A2B20.2BA2B18.7B11.5B8.2A$132.2A173.3A5.4B5.4B2.BA3BA2B
.B2A30.2B11.2A3.A.A4.12B9.2AB.7BAB2A.2ABA7B.B2A8.3BA3B20.7B2A7B18.A4B
21.5B19.4B14.2B$132.A176.A6.4B5.5BA5BA3B51.A5.12B8.A.AB2.6B3AB.B3A6B2.
BA.A7.2BABA2B20.2A3.BA2BAB3.2A19.BA2B.B20.B3A17.5B14.2A$133.A183.4B5.
4BA5BA3B57.13B7.A6.6BA2B.2BA6B6.A8.2BA2B22.A3.2B2A2B3.A20.2A3B2A21.B18.
2A17.A$123.2A7.2A184.4B5.3BA5BA3B57.13B6.2A8.7B.7B8.2A7.2BA2B19.3A14.
3A17.B2ABABA41.A18.A$123.A2.AB.2BA187.4B5.3BA3BA2B10.2A47.13B16.7B.7B
18.3B20.A18.A17.2B4A39.3A18.2A$124.2A2B2A2B2A186.4B2.6B3A3B2.B.B5.A50.
10B18.6B.6B19.3B59.B2AB39.A$126.A2B.BA2.A186.23B.BA.A51.6B.4B17.5B.5B
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.A4.A17.B2AB2.B14.A.A2.A.A11.BAB21.M23.2A35.A.A6.A.A2.A.A260.4B10.4B$
20.A36.16B11.2A3.A.3A18.3B2.3B2.2B11.A2BA13.BA20.M61.A.A.A7.A2BA263.2B
AB10.4B$20.4A33.16B10.A2.3AB.A21.B.10B8.BA4BAB12.2A19.5M19.4A34.A.B.A
5.BA4BAB262.2B2A10.2B2A$23.A30.B.4B2ABA2BAB2A4B.B8.A.A2.BA20.5B2A7B.2B
5.B2A2B2AB12.2B.A22.M18.A2.AB25.2A4.2A.2A.2A4.BA4BAB263.2A2B10.BABA$18.
3AB31.2A4BA2BA4BA2BA4B2A6.2A2.2A2B3.2A14.7B2A8B2A5.2B2A2B3.2A7.A4BA18.
3M20.4B25.A2.A.A.A.B.A7.A4BA265.4B10.A3B$7.2A8.A2.AB31.2A5BABA4BABA5B
2A8.A.A2.B2.B2AB13.15B.B2A7.2B4.B2AB7.2B.BA6.A10.M21.6B27.2A.A.B.C.A9.
2A268.4B5.A4.4B$7.A.A2.2A3.2A.2B32.7BA6BA7B9.A.A3.B2.2B15.15B.B9.D5.2B
8.3A6.3A10.4M17.12B23.A.A2B2A.2A9.D269.4B4.3A3.4B$4.A4.A3.A6.3B31.22B
10.A3.A2B.B16.7BABA5B12.A2BA2B10.B6.A11.2M3.M10.A6.13B10.A7.B.B2A.B.A
2.A12.B3.B265.4B6.A3.4B$4.5A.3A7.4B32.7B4.7B15.A.A4B14.7BA3BA5B8.A6BA
2B10.D5.2A9.M2.3M11.3A4.8BA5B9.3A4.2A4B2A.2A.A11.7B265.4B4.2A4.4B$8.A
.A8.7B64.AB.B3A2B10.7BAB.BA7B6.A7BA2B4.B5.2B.5B9.2M.M16.A3.9BA3B13.A2.
B2AB.B2.BA2.A9.2B.B2A4B.2B263.4B2.2B6.4B10.2A$4.3ABABA6.9B30.7B4.7B19.
5BAB10.5BA3BA7B8.AB2A3BAB.2B.B2A4.4BAB14.M15.2A3.6BA2BA3B12.2A3.2B8.A
9.2A2B2ABA5B2A255.2A6.8B6.4B2.2B4.B2A2B$3.A2.AB2A17B27.22B16.2BA4BAB10.
5BABA7B9.4B3A2.5B2A3.4BABAB13.2M14.11B3A5B11.6B10.3A6.2AB.BABA3B.B2A256.
A7.7B7.10B2.4B$3.2A2.2B.18B26.7BA6BA7B16.2BA3BA2B8.B.15B10.6B2.3AB.B3.
4BA3BAB30.17B13.5B5.2A4.A7.B.4BA4B.B257.A.2A5.7B2.B2.11B.B.4B$10.18B25.
2A5BABA4BABA5B2A16.2BA3BA2B6.2AB.15B15.BA3BA6.3BA2BA4B27.17B8.2A3.6B5.
A16.3B.BAB261.A2.A4.29B$8.B2.11B2A6B2.4B17.2A4BA2BA4BA2BA4B2A16.BA4BA
2B6.2A8B2A7B15.BA4B6.3BA2BA5B25.18B8.A4.B.5B.BA.A285.2AB3.30B$7.2AB.10B
ABA13B9.A7.B.4B2ABA2BAB2A4B.B18.BA5B8.2B.7B2A5B16.BA4B7.3B2A5B25.2A16B
11.A.8B.B2A17.3B.BAB263.36B3.2A$7.2A11B2A15B7.3A10.16B22.2B3AB.BA8.10B
.B18.2BA2BA7.8B26.A.AB.14B10.2A6BA4B16.B.4BA4B.B261.14BA14B2A4B.B2.A$
8.2B.10BABA12B7.A13.16B25.4BA.A8.2B2.3B2.3B17.2BA2B8.9B25.A5.3B.B2.5B
10.A3.3B3A4B15.2AB.BABA3B.B2A261.12B3A12BABA5B3A$11.11B2A14B5.2A13.14B
27.B.2BA14.B2.B2AB17.5B9.8B24.2A5.2B8.4B7.A.2A4BABA4B15.2A2B2ABA5B2A261.
9B3AB2A2B.B6.BABA2B2.2BA$12.4B.21B2.5B18.4B31.2B2.B19.2A19.BABA9.9B42.
2A6.A2.A.AB.3BA3B17.2B.B2A4B.2B263.8BA6B10.BA2B6.2A$10.5B2.21B.4B21.2B
31.B2AB44.A11.8B42.A7.2A2.AB3.6B20.7B266.15B21.A$10.2A5.14B2A11B18.BA
2BAB30.2A55.5B2A3B43.3A14.5B21.B3.B268.13B21.A$11.A7.12BABA10B.2B14.3A
2B3A85.5BA2BA3B44.A12.5B.B2A294.13B19.2A$8.3A7.15B2A11B2A13.B2A2B2AB86.
4BA2BA3B57.2A4.BA.A292.8B4.2A.A$8.A9.13BABA10B.B2A15.A2BA90.BA3BA4B57.
A7.A292.6B6.2AB3A$19.4B2.6B2A11B2.B14.A.A2.A.A89.BABA4B55.3A8.2A291.5B
8.B4.A$27.18B16.2A4.2A90.BA4B56.A303.B.B9.2A.3A$27.18B.2B2.2A105.5B.2B
361.3B9.A.A$28.17B2ABA2.A105.2A366.B2AB9.A.A$29.9B6.ABAB3A107.A367.2A
11.A$29.7B8.A.A108.3A$31.4B7.3A.5A104.A$32.3B6.A3.A4.A$33.2B.2A3.2A2.
A.A$33.BA2.A8.2A$33.B3A$31.A$31.4A$34.A$33.A$33.2A!

[Period1GliderGun]

73P260:

Code: Select all

x = 24, y = 23, rule = B3/S23
2bo$2b3o$5bo9b2o$4b2o9bo$13bobo$13b2o3$6b3o$6bo2b2o$6b2o2bo$2b2o4b3o$
bobo11b2o$bo9b2obobo$2o9b2obo2b2obo$15bobob2o$11b2ob2o5b2o$11bo4bob3o
2bo$12b3obo4b2o$14b2o2bobo$18bobo$14b2o3bo$14b2o!

EDIT: 77P364:

Code: Select all

x = 32, y = 30, rule = B3/S23
14b2o$16bo$13bo2bo$13bo$5b2o$4bo2bo6bo2b2o11b2o$4b2obo5b5o12bo$2b3obo
5b2o5bo8bobo$bobo8bo5b2o5bob3o$bo12b5o5bob2o$2o11b2o2bo6bo2bo$25b2o$18b
o$9bo5bo2bo$9b3o3bo$12bo3b2o4b2o$11b2o9bo$16bo2b2obo$17bo3bo$13b2o$12b
o3bo$13b2o3b2o$13b2o$16b2o$9b2o$8bobo$8bo9b2o$7b2o9bo$19b3o$21bo!

[Period1GliderGun]

Apologies for the double post. If I find more LCMs I'll edit this post.
57P176; the one on the wiki has a minpop of 59

Code: Select all

x = 35, y = 11, rule = B3/S23
26bo$2o24bo3b5o$bo24bo2bo3b2o$bobo13b3o8bo$2b2o3bo8bo3bo7b2o$6bob2o6b
o4bo11bo$5bo4bo6b2obo7b2ob2o$6bo3bo8bo3b2o3b2o$7b3o13bobo$25bo$25b2o!

EDIT: 61P208 (previous: Charity's p16 deleting blocks from p52 LoM hassler, 78 cells)

Code: Select all

x = 23, y = 24, rule = B3/S23
12bo$12b2o$12b2o$13bo$16b2o3bo$15bo2bobobo$11bo3bo5bo$10bobo2b2o$6b2o
3bo$6b2o11bo$19b2o$19b2o$7bobo5bo4bo$7bo3bo3bo$2o5bo4b2obo$2o2b3o5bo$
9b2o$4bo3bo$8bo$5bo$6b2o$6bo2$4b3o!

96P273 (previous: caterer on p91 R hassler)

Code: Select all

x = 31, y = 31, rule = B3/S23
17bo$5bo9b3o$4bobo7bo$4bobo7b2o$2b3ob2o$bo$2b3ob2o10b2o$4bob2o9bo$11b
o8bo2b4o$11b2o8b3o2b4o$10bobo6b2ob2o2b3obo$11bo8bo8bo$20bob5o$21b2o2$
6b2o$6b2o3$7bobo5bo$7bo3bo3bo$2o5bo4b2obo$2o2b3o5bo$9b2o$4bo3bo$8bo$5b
o$6b2o$6bo2$4b3o!

EDIT2: Some multiples of 37 (and other primes).
85P407 (previous: rectifier loop)

Code: Select all

x = 36, y = 26, rule = B3/S23
17bo$17b3o14b2o$20bo13bo$19b2o11bobo$32b2o$24b2o$24b3o$23bo2bo$24b2o$
9b2o$10bo$10bobo19b2o$7bo3b2o19bobo$6bobo25bo$7bo26b2o$19b2o$5b5o3b2o
3bo2bo$4bo5bo2b2o3b3o$3bob2obo2bo7b2o$3bobobo$2obobobo16b2o$2obobobo16b
o$4bo6bo13b3o$9b2obo14bo$12bo$12b2o!

93P333 (previous used 43P9 and was one cell larger)

Code: Select all

x = 35, y = 29, rule = B3/S23
16bo$16b3o14b2o$19bo13bo$18b2o11bobo$31b2o$23b2o$23b3o$22bo2bo$23b2o$
8b2o$9bo$9bobo19b2o$10b2o19bobo$33bo$33b2o$18b2o$12b2o3bo2bo$b2o4b2o3b
2o3b3o$bobo3bo2bo7b2o$3bo$3b3o5bo11b2o$b2o3bobo2bo11bo$o2b2o19b3o$b2o
3b5o15bo$3b2obo5bo$3bo2bob5o$4bobobo$5bo4bo$9b2o!

128P559 (previous: rectifier loop)

Code: Select all

x = 37, y = 43, rule = B3/S23
12b2o$12b2o2$15bo2bo$14bo6bo$14bo7bo$6b2o6bo3b2obo$6b2o7b3o$10b3o$9bo
3bo$13bo$4b2o7bo$4bobo2bo2bo$5b3o4bo$6b2o$4bobo3bobo$3bob2o4bo$3bo$2o
bo11b2o$2ob2o10bobob2o$17bobobo7bo$16bo2bo2bo5bobo$16b2o2b2o7bo3$5b2o
$6bo6bo14bo$6bobo3b3o12b3o$7b3ob5o10b5o$9b3o3b2o8b2o3b2o$9b3o3b3o6b3o
3b3o$10b2o3b2o8b2o3b3o$11b5o10b5ob3o$12b3o12b3o3bobo$13bo14bo6bo$35b2o
3$12bo7b2o2b2o5b2o$11bobo5bo2bo2bo5bobo$12bo7bobobo8bo$21b2obobo6b2o$
25b2o!

126P423 (previous used 48P9, 132 cells)

Code: Select all

x = 36, y = 37, rule = B3/S23
6bo$5bobo2b2o$5bobo3bo$3b2obob3o$2bobobobo$bo6bo$2b4obo$5bo4b2o4bo7bo
$2b2obobo3bo3bobo5bobo$o2bobo10bo7bo9b2o$2obobo4bo23bo$3bo3b2o23bobo$
3b2o27b2o$11bo4b3o3b3o4bo$11bo4b3o3b3o4bo$11bo5bo5bo5bo$7b2o$6bobo$6b
o$5b2o2$12b2o13b2o$12b2o13b2o6$11bo5bo5bo5bo$11bo4b3o3b3o4bo$11bo4b3o
3b3o4bo$7b2o23b2o$6bobo23bobo$6bo27bo$5b2o9bo7bo9b2o$15bobo5bobo$16bo
7bo!

EDIT3: 108P295; for some reason the SKOP table has 108P59 instead of 92P59

Code: Select all

x = 43, y = 43, rule = B3/S23
21b2o$22bo$22bobo$23b2o2b3o5$26bo8bo2bo$25bobo6bob2obo$25bobo7bo2bo$26b
o8bo2bo$22b2o10bob2obo$3bo17bobo11bo2bo$3bo17bobo$3bo5b2o11bo$8bo2bo$
9b2o$2b2o$3bo8b3o$3o9bo2bo$o12b2o13b2o12bo$27bo2bo9b3o$28b3o8bo$39b2o
$32b2o$31bo2bo$20bo11b2o5bo$19bobo17bo$19bobo17bo$19b2o$16bo$15bobo$15b
obo$16bo5$13b3o2b2o$18bobo$20bo$20b2o!

EDIT4: 109P319 (previous: rectifier loop)

Code: Select all

x = 28, y = 36, rule = B3/S23
25bo$24bobo$19bo4bobo$13bob2o4bob2ob2o$13b2obo5bo2bo$23bobo$21bo2bo$13b
2o3bo2b3o$13b2o5bo$22b2o$23bo$10b2o10bo$10bobo9b2o$11bobo$12bo$12bo3b
2o$11bo4bobo$2bo8bo6bo$bobo14b2o$2bo4b3o$9bobo$11bo3b2o$15bobo$9bo7bo
$2o5bobobo5b2o$2o3b3o3b3o$11b2o$11b2o5b2o$10b3o2b2o2bo$10b2o2bob3o$11b
4o$8bo6b4o$8b6obo2bo$12bobo$10bo$10b2o!

85P350 (previous: 34P14 on p50 pi hassler, 94 cells)

Code: Select all

x = 35, y = 28, rule = B3/S23
15bo$15b3o$18bo$17b2o2$21b2obo$19b2obo2bo$18bo3bo2bo$23b3o$18bo11bo$19b
o11bo$15bo8b3o$15bo8bo2bo3bo$24bo2bob2o$25bob2o$5b2o$5bobo5b3ob2o12b2o
$6b2o4bo18bo$2b2o7b2o19b3o$bobo15b2o4bo3bo4bo$bo17bo4bobo3bo$2o11b2ob
3o5bo5bo$25b5o2$25b2o3b2o$16bo8bo4bo$16bo9bo4b3o$25b2o6bo!

[WhiteHawk]

The 38-cell p5 thumb allows for a smaller p5 Gallus reaction (shown with a reduction to SKOP 250, from 119 to 112 cells)

Code: Select all

Are there other SKOP reductions using this shuttle besides SKOP250?

Also enjoying you great SKOP finds, but could you please mention what the SKOPs were before just for reference?

EDIT: 2 years on, and the wiki STILL hasn't been updated

P598, minimum phase is 62 cells:

Code: Select all

[WhiteHawk]

Doublepost for actual SKOPs & for putting it out there that User:Galoomba/Skopje (a good source for SKOPs over 106) is over a year out of date

102p511 (beating 136-cell rectifier) - 34p7 on p73 LOM with interesting reaction

Code: Select all

x = 35, y = 47, rule = B3/S23
16bo2bo$15bo$14bo5bo$14bo4b2o$15bo$16bo$12bob4o$13bo3bo$15bo3bo$15b4o
bo$16bo$17bo$12b2o4bo$12bo5bo$bo15bo$b3o9bo2bo$4bo$3b2o6$22bo$21bobo3b
2o$22bo4bobo$8b3o18bo$8bobo17b2ob2obo$8bo2bo19bob2o$9bobo19bo$3b2o4b3o
11b3o4b2o$3bo19bobo$2obo19bo2bo$ob2ob2o17bobo$5bo18b3o$5bobo4bo$6b2o3b
obo$12bo6$30b2o$30bo$31b3o$33bo!

98p581 (beating another rectifier) - 34p7 on tub-supported 62p83

Code: Select all

x = 42, y = 33, rule = B3/S23
5bo$2o3b2o$2o3b2o$5bo$3bo2bo$3bob3o$2b2o3bo17b2o$bo3b2o5b2o11bo$b3obo
7bo9bobo$2bo2bo7bobo7b2o$3bo10b2o$2b2o3b2o22b2o$2b2o3b2o23bo$3bo25b3o
$29bo3$6bo12bo$5bobo9b2ob2o$6bo13bo5bo13bo$25b2ob2o9bobo$27bo12bo3$17b
o$15b3o$14bo$14b2o$31b2o$22b2o7bobo$21bobo9bo$21bo11b2o$20b2o!

EDIT: BB reduction to the first one while attempting to expose a spark

Code: Select all

x = 35, y = 39, rule = B3/S23
19bo5b2o$20bo4bo2bo$15b2o2bo$14bo2bobob2o$13bo4b2o2b2o4bo$19b2obobo2b
o$bo20bo2b2o$b3o9bo2bo4bo$4bo10b2o5bo$3b2o6$22bo$21bobo3b2o$22bo4bobo
$8b3o18bo$8bobo17b2ob2obo$8bo2bo19bob2o$9bobo19bo$3b2o4b3o11b3o4b2o$3b
o19bobo$2obo19bo2bo$ob2ob2o17bobo$5bo18b3o$5bobo4bo$6b2o3bobo$12bo6$30b
2o$30bo$31b3o$33bo!

p4088 oscillator I got from this (EDIT 2: Not SKOP. All 64+8n oscillators have minipop of at least 92 cells as a result of the p8 shuttle)

Code: Select all

x = 35, y = 41, rule = B3/S23
3b2o2$bo3bo13bo5b2o$bo4bo13bo4bo2bo$3bobobo7b2o2bo$4bobobo5bo2bobob2o
$5bo4bo2bo4b2o2b2o4bo$6bo3bo8b2obobo2bo$bo20bo2b2o$b3o3b2o4bo2bo4bo$4b
o10b2o5bo$3b2o6$22bo$21bobo3b2o$22bo4bobo$8b3o18bo$8bobo17b2ob2obo$8b
o2bo19bob2o$9bobo19bo$3b2o4b3o11b3o4b2o$3bo19bobo$2obo19bo2bo$ob2ob2o
17bobo$5bo18b3o$5bobo4bo$6b2o3bobo$12bo6$30b2o$30bo$31b3o$33bo!

EDIT 2:

This gives oscillators with at most 128 cells for all periods of the form 3*(4n+1).

Not quite. The design doesn't work for periods where 4n+1 is a multiple of 3. For those values of n where 4n+1=3m is not also a multiple of 5 (therefore also being a multiple of 15) or upstaged by other SKOPs the 136-cell rectifier still stands as SKOP for those periods. However, it does usurp all 136-cell rectifiers which have periods 3*(4n+1) where 4n+1 is not a multiple of 3 (which needs to be acknowledged on the page linked at the top)

[KtT]

SKOP 378, minimum phase is 70 cells:

Code: Select all

x = 31, y = 30, rule = B3/S23
20bo$9b2o7b3o$9b2o6bo$17b2o2$2o22b2o$bo8bo13bo$bobo6b2o10bobo$2b2o5bo
2bo9b2o$10b2o3$24b2o$3b2o19b2o$5bo$2bo26bo$3b2o23bobo$29bo2$20b2ob3o$
19bo2bo3bo$19bo3bo2bo$20b3ob2o2$16bo$15bobo$16bo2$20b2o$20b2o!

Former SKOP 378:

Code: Select all

x = 38, y = 21, rule = B3/S23
17bo$17b3o7b2o$20bo6b2o$19b2o2$12b2o22b2o$13bo22bo$13bobo10b3o5bobo$14b
2o10bo7b2o$26b2o3$11b2o$4b3o4b2o20bo$o6bo25b2o$o2bobob2o24b2o$b3o6b3o
21bo$5b2obobo2bo$6bo6bo$b2o4b3o$b2o!

[WhiteHawk]

SKOP 378, minimum phase is 70 cells:

Code: Select all

I'll do you one better - twice! SKOP 378 is now 69 cells

Code: Select all

x = 31, y = 30, rule = B3/S23
20bo$9b2o7b3o$9b2o6bo$17b2o2$2o22b2o$bo8bo13bo$bobo6b2o10bobo$2b2o5bo
2bo9b2o$10b2o3$24b2o$3b2o19b2o$5bo$2bo26bo$3b2o23bobo$29bo$24bo$20b6o
$19bob2o3bo$19bo3b2obo$20b6o$21bo$16bo$15bobo$16bo2$20b2o$20b2o!

Code: Select all

x = 31, y = 30, rule = B3/S23
20bo$9b2o7b3o$9b2o6bo$17b2o2$2o22b2o$bo8bo13bo$bobo6b2o10bobo$2b2o5bo
2bo9b2o$10b2o3$24b2o$3b2o19b2o$5bo$2bo26bo$3b2o23bobo$29bo$21b2ob2o$20b
o3b2o$19bo6bo$19bo6bo$20b2o3bo$20b2ob2o$16bo$15bobo$16bo2$20b2o$20b2o
!

[C_R_116]

14-cell SKOP 219 reduction:

Code: Select all

x = 33, y = 40, rule = B3/S23
18b2o$2o16bo$bo17bo$bobo12b4o$2b2o12bo$19b3o$19bo2bo$21b2o2$12b3o$15bo
$13bobo6bo$14bo6bobo$22bo8$10bo$9bobo6bo$10bo6bobo$17bo$18b3o2$10b2o$
10bo2bo$11b3o$16bo12b2o$13b4o12bobo$13bo6b3o8bo$14bo3bo12b2o$13b2o3bo
4bo$19bo$21b2o$22bo$22bo$22bo!

[WhiteHawk]

The 38-cell p5 thumb allows for a smaller p5 Gallus reaction (shown with a reduction to SKOP 250, from 119 to 112 cells)

Code: Select all

Reduced by 2 cells using 37-cell p5 version (112 -> 110) which sparks in a different place

Code: Select all

x = 50, y = 42, rule = B3/S23
8b2o4bo$8b2o3bobo$14bo3$b2o2b2o$b2o2b2o5$2o2b2o2bo$o2bobob2o$bob3obo$
2bo2b3o$3b3ob2o2$3b3o$2bo3bo$2b2o3b2obo$9bobo27bo$10bo27bobo$39bob2o3b
2o$43bo3bo$44b3o2$41b2ob3o$42b3o2bo$42bob3obo$41b2obobo2bo$41bo2b2o2b
2o$37bo$38bo$36b3o2$43b2o2b2o$43b2o2b2o3$35bo$34bobo3b2o$35bo4b2o!

EDIT: These two replace 113-cell 1g rectifiers (all rectifiers of the form 10+40n can be usurped by this design and the 38-cell version)

SKOP 610 - 110 cells

Code: Select all

x = 95, y = 87, rule = B3/S23
8b2o4bo$8b2o3bobo$14bo3$b2o2b2o$b2o2b2o5$2o2b2o2bo$o2bobob2o$bob3obo$
2bo2b3o$3b3ob2o2$3b3o$2bo3bo$2b2o3b2obo$9bobo$10bo44$84bo$83bobo$84bo
b2o3b2o$88bo3bo$89b3o2$86b2ob3o$87b3o2bo$87bob3obo$86b2obobo2bo$86bo2b
2o2b2o$82bo$83bo$81b3o2$88b2o2b2o$88b2o2b2o3$80bo$79bobo3b2o$80bo4b2o
!

SKOP 650 - 110 cells

Code: Select all

x = 100, y = 92, rule = B3/S23
8b2o4bo$8b2o3bobo$14bo3$b2o2b2o$b2o2b2o5$2o2b2o2bo$o2bobob2o$bob3obo$
2bo2b3o$3b3ob2o2$3b3o$2bo3bo$2b2o3b2obo$9bobo$10bo49$89bo$88bobo$89bo
b2o3b2o$93bo3bo$94b3o2$91b2ob3o$92b3o2bo$92bob3obo$91b2obobo2bo$91bo2b
2o2b2o$87bo$88bo$86b3o2$93b2o2b2o$93b2o2b2o3$85bo$84bobo3b2o$85bo4b2o
!

[WhiteHawk]

Unrelated, but I think this LCM beats out the 136-cell rectifier for SKOP 603 by two cells (134 cells)

Code: Select all

x = 62, y = 49, rule = B3/S23
45bo$45b3o$48bo$47b2o$19bo6b2o$19b3o4b2o28b2o$22bo33b2o$13bo7b2o16b3o
$13b3o21bob3o$16bo19bo$15b2o18b2o$36b2o$37bo$2b2o$3bo$3bobo$4b2o7$58b
2o$58bobo$60bo$60b2o$26bo$26b2o$27b2o18b2o$27bo19bo$22b3obo21b3o$22b3o
16b2o7bo$6b2o33bo$6b2o28b2o4b3o$36b2o6bo$15b2o$15bo$16b3o$18bo$3b2o$3b
obob2o2b2o$2obobobobo2bo$2obo3bob3o$3bo3bo$3bobob3o$4bobo3bo$6bo2b2o$
6b2o!